Class 09 To verify the algebraic identity : (a + b)2 = a2 + 2ab + b2

 Activity 3 

OBJECTIVE               

          

                                            

To verify the algebraic identity : (a + b)² = a² + 2ab + b²

 MATERIAL REQUIRED

 Drawing sheet, cardboard, cello-tape, coloured papers, cutter and ruler.

 METHOD OF CONSTRUCTION

 1.   Cut out a square of side length a units from a drawing sheet/cardboard and name it as square ABCD [see Fig. 1].

 2.   Cut out another square of length b units from a drawing sheet/cardboard and name it as square CHGF [see Fig. 2].

 Fig. 1                                                                             Fig. 2

 3.   Cut out a rectangle of length a units and breadth b units from a drawing sheet/cardbaord and name it as a rectangle DCFE [see Fig. 3].

 Cut out another rectangle of length b units and breadth a units from a drawing sheet/cardboard and name it as a rectangle BIHC [see Fig. 4].

5.   Total area of these four cut-out figures

 =  Area of square ABCD + Area of square CHGF + Area of rectangle DCFE

 +  Area of rectangle BIHC

 =  a² + b² + ab + ba = a² + b² + 2ab.

 Join the four quadrilaterals using cello-tape as shown in Fig. 5.

Clearly, AIGE is a square of side (a + b). Therefore, its area is (a + b)². The combined area of the constituent units = a² + b² + ab + ab = a² + b² + 2ab.

 Hence, the algebraic identity (a + b)² = a² + 2ab + b² Here, area is in square units.

 OBSERVATION

 On actual measurement:

 a = ..............,     b = .............. (a+b) = ..............,

 So, a² = ..............        b² = .............., ab = ..............

 (a+b)² = ..............,             2ab = ..............

 Therefore, (a+b)² = a² + 2ab + b² .

 The identity may be verified by taking different values of a and b.

 APPLICATION

 

The identity may be used for

 

1.   calculating the square of a number expressed as the sum of two convenient numbers.

 

2.   simplifications/factorisation of some algebraic expressions.